Bayesian Statistics the Fun Way – Book Solutions and Notes

Notes and solutions for “Bayesian Statistics the Fun Way” by Will Kurt, No Starch Press, 2019.

Chapter 19: From Hypothesis Testing to Parameter Estimation

Our Bayes factor assumed that we were looking at \(H_1: P(\text{prize} = 0.5)\). THis allowed us to derive a version of the beta distribution with an alpha of 1 and a beta…

Chapter 18: When Data Doesn’t Convince You

When two hypothesis explain the data equally well, one way to change our minds is to see if we can attack the prior probability. What are some factors that might increase…

Chapter 17: Bayesian Reasoning in the Twilight Zone

Every time you and your friend get together to watch movies, you flip a coin to determine who gets to choose the movie. Your friend always picks heads, and every Friday for…

Chapter 16: Introduction to the Bayes factor and posterior odds

Recall that from Bayes’ theorem, \[P(H \mid D) \propto P(H) \times P(D\mid H).\] If we want to compare the relative likelihood of two events, we do not need the normalizing…

Chapter 15: From Parameter Estimation to Hypothesis Testing

Suppose a director of marketing with many years of experience tells you he believes very strongly that the variant without images (B) won’t perform any differently than the…

Chapter 14: Parameter Estimation with Prior Probabilities

Suppose you’re playing air hockey with some friends and flip a coin to see who starts with the puck. After playing 12 times, you realize that the friend who brings the coin…

Chapter 13: The Tools of Parameter Estimation

Using the code example for plotting the PDF on page 127, plot the CDF and quantile functions.

Chapter 12: The Normal Distribution

This chapter introduces the normal distribution. There’s not much else to say about it.

Chapter 11: Measuring the Spread of Our Data

This chapter defines the mean absolute deviation (MAD), variance, and standard deviation of a set of numbers.

Chapter 10: Introduction to Averaging and Parameter Estimation

This chapter covers the basics of parameter estimation, particularly focusing on how to compute unweighted and weighted averages (resulting in the formula for the discrete…

Chapter 9: Bayesian Priors and Working with Probability Distributions

This chapter introduces the concept of a prior probability distribution, rather than a single point prior (which is also, technically, a prior distribution, but it is the…

Chapter 6: Conditional Probability

This chapter introduces the concept of conditional probability, which, in my opinion, is one of the least intuitive parts of probability. I didn’t take a lot of notes here…

Chapter 5: the Beta Distribution

I actually took notes this time! I already know a pretty good amount about the beta distribution, but I’ve never used it like this before.

Chapter 4: Creating a Binomial Probability Distribution

My original intention was also to post all of the notes I took while reading through this book. But we’re still in stuff that I felt pretty comfortable with (because I’ve…

Chapter 8: Priors, posteriors, and likelihoods of Bayes’ Theorem

This chapter is mostly about Bayes’ factors without saying that it’s about Bayes factors, but it also discusses what happens when prior beliefs change (in a particularly…

Chapter 7: Bayes’s Theorem with LEGO

Again, no notes. Mostly because this chapter is super short. Just for good measure, I’ll do the mathematician thing and say. Recall Bayes’ Theorem:

Chapter 3: The Logic of Uncertainty

What is the probability of rolling a 20 three times in a row on a 20-sided die?

Chapter 2: Measuring Uncertainty

What is the probability of rolling two six-sided dice and getting a value greater than 7?

Chapter 1: Bayesian Thinking and Everyday Reasoning

I already have a math degree where I focused on stats, so I kind of rushed through this chapter.